This is an economics question required to solved by hand

1. For each of the following functions, (i) compute the first derivative, (ii) compute the second derivative, (iii) indicate whether the function is strictly concave, strictly convex, or neither (explain your reasoning), (iv) indicate whether it is homogeneous or not. (a) f(x) = In(x2 + x) (b) f(x) = V(x+2)2+3 (c) f(x) = (x2 -2x +1) - (x -1)2 (d) f(x) = x 2. A consumer with utility function u(x, y) = vay has an income of $15 and the price of good x is $5 and the price of good y is $3. Assume that he has to consume all of his income. (a) Write down the utility maximization problem subject to his budget constraint. (b) Write down the First order conditions for the maximization problem. (c) Determine the solution to this maximization